Question: Evaluate $\left\lceil\sqrt{140}\right\rceil$.
Explanation: The value $\sqrt{140}$ lies between the two nearest integers.  Let the two nearest integers be $z_1$ and $z_2$.  Then we have $$z_1<\sqrt{140}<z_2$$Because all values in the inequality are positive, it is appropriate to square each value and obtain $$z_1^2<140<z_2^2$$We only need the value of the perfect square greater than 140, which is 144.  Thus the least integer greater than $\sqrt{140}$ is $\sqrt{144}=\boxed{12}$.